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Relatively Free Semigroups of Intermediate Growth

L.M Shneerson
2001 Journal of Algebra  
One of the main purposes of this paper is to give examples of relatively Ž . free semigroups and monoids having intermediate growth Section 6 .  ...  Quite recently our methods helped us to construct examples of relatively free semigroups of Ž . intermediate growth and maximal equals 1 Gelfand᎐Kirillov superdimension.  ...  The equality 160 shows that induces a one-to-one correspondence Ä 4 between the set of all finite sequences ␣ as above and the set of all n words of the type ⌬ U over the alphabet ⌽.  ... 
doi:10.1006/jabr.2000.8503 fatcat:5l2omizwljdpvm2qqnf6tokhzy

Page 2861 of Mathematical Reviews Vol. , Issue 97E [page]

1997 Mathematical Reviews  
Mat. 54 (1990), no. 5, 899-927; MR 92h:16020] the author presents the following broad result: if T is the semigroup of automorphisms of a free countably generated algebra over a field of characteristic  ...  0, and R is a relatively free algebra satisfying a standard identity, then R is Noetherian as an F[7]-module.  ... 

Growth, unavoidable words, and M. Sapir's conjecture for semigroup varieties

L.M. Shneerson
2004 Journal of Algebra  
Some applications including examples of f.g. relatively free semigroups having intermediate growth and maximal (equals 1) superdimension are considered. 483 Let U be a word over the alphabet Λ and W a  ...  Furthermore, the length of the period is bounded above by a constant which depends only on the number n and on the number of generators of S.  ...  We also find the first example of a relatively free f.g. semigroup which has intermediate growth and superdimension 1 (Theorem 4.1) and a similar example of a semigroup which is nilpotent in the sense  ... 
doi:10.1016/j.jalgebra.2003.09.021 fatcat:ggdkpnq4cna3begbds2tc24vdi

On generating functions for subalgebras of free Lie superalgebras

V.M. Petrogradsky
2002 Discrete Mathematics  
But the appropriate formula exists in terms of formal power series. The result is obtained in generality of free Lie superalgebras, graded by some semigroups.  ...  In this case instead of formal power series we use elements of the completion of a semigroup ring, which are called characters.  ...  In particular, this is the case, if A is a relatively free superalgebra of some variety with the generating set X = X + ∪ X − .  ... 
doi:10.1016/s0012-365x(01)00262-x fatcat:ewc4vask4nekxjwqg4fzjoj42i

Monomial algebras

A. Ya. Belov, V. V. Borisenko, V. N. Latyshev
1997 Journal of Mathematical Sciences  
relatively free) algebras.  ...  A.A.Kirillov and M.L.Koncevich [26] constructed a relatively free Lie algebra of an intermediate growth: the Lie algebra of generic vector elds on a variety.  ...  The method of generalization uses the passage to an associative algebra of (left)  ... 
doi:10.1007/bf02355446 fatcat:zt4izxi4yzhd7mx5o7lufa2ika

From minimal geodesics to supersymmetric field theories [chapter]

Henning Hohnhold, Stephan Stolz, Peter Teichner
2010 CRM Proceedings and Lecture notes AMS  
For example, the maximal number of independent vector fields on the n-sphere was determined explicitly.  ...  From these classical descriptions we move via spaces of unbounded operators and super-semigroups of operators to our most recent model, which is given by certain spaces of supersymmetric (1|1)-dimensional  ...  referred to as the superdimension.  ... 
doi:10.1090/crmp/050/20 fatcat:s3kjzsqnznaupldmukl7y6phym

Schild Action [chapter]

Yolanda Lozano, Steven Duplij, Malte Henkel, Malte Henkel, Euro Spallucci
2004 Concise Encyclopedia of Supersymmetry  
Semigroup congruences are important for the study and classification of complex physical phenomena, especially when applied to free semigroups and monoids. Bibliography [1] A. H. Clifford and G. B.  ...  T from the set of elements of semigroup S into the set of elements of semigroup T such that /ðxyÞ ¼ /ðxÞ/ðyÞ for all x; y 2 S. When / is bijective, then S and T are isomorphic semigroups.  ...  A simple example is the following one for a free model of where Q BRS ic a k a ; @t . This is an N ¼ 2 supersymmetry.  ... 
doi:10.1007/1-4020-4522-0_474 fatcat:f42ycwddmjbqva6u6dtues4ig4

A Cyclic Orbifold Theory for Holomorphic Vertex Operator Algebras and Applications [article]

Sven Möller
2017 arXiv   pre-print
We use these results to construct five new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds, contributing to the classification of the V_1-structures of suitably regular,  ...  To this end we describe the fusion algebra of the fixed-point vertex operator subalgebra V^G and show that V^G has group-like fusion.  ...  I enjoyed working together with both of them on the paper [EMS15] , which is partly based on this dissertation and vice versa.  ... 
arXiv:1611.09843v2 fatcat:ni2mohubjje67gcix7t5dtfeyq